Step 1: We need to find the slope of the given line. In order to find the slope, we need to rewrite the equation in slope-intercept form, y=mx+b, where m represents the slope and b the y-intercept.
So, we start with our given equation, 7x + 4y = 9. We should isolate y to put the equation in the form y = mx + b.
Doing so gives us 4y = -7x + 9, which simplifies further to y = -7/4*x + 9/4.
From this equation, we can see that the slope (m) of the line is -7/4 or -1.75.
Step 2: If a line is parallel to another line, it means they have the same slope. So, the slope of any line parallel to the original one equals the original slope of -1.75.
Step 3: Lines are perpendicular to each other if their slopes are negative reciprocals. So, to find a slope of a line that is perpendicular to the original, we take the negative reciprocal of the original slope.
Reciprocal of -7/4 is -4/7 and negation gives us 4/7 which is approximately equal to 0.57.
Therefore, the slope of any line parallel to the original line is -1.75 and the slope of any line perpendicular is approximately 0.57.